Whittaker-Shintani functions for Fourier-Jacobi models on unitary groups

TL;DR

This paper establishes a formula for Whittaker-Shintani functions related to Fourier-Jacobi models on p-adic unitary and general linear groups, crucial for the Gan-Gross-Prasad conjecture and the unramified Ichino-Ikeda conjecture.

Contribution

It provides the first explicit formula for Whittaker-Shintani functions in this context, advancing the understanding of Fourier-Jacobi models and their applications.

Findings

Proved a formula for Whittaker-Shintani functions on p-adic groups.

Applied the formula to confirm the unramified Ichino-Ikeda conjecture.

Enhanced the proof of the Gan-Gross-Prasad conjecture for Fourier-Jacobi models.

Abstract

We state and prove a formula for the Whittaker-Shintani functions associated to Fourier-Jacobi models for p-adic unitary groups and general linear groups. These generalized spherical functions play a fundamental role in the proof of the Gan-Gross-Prasad conjecture for Fourier-Jacobi models. As an application we prove the unramified Ichino-Ikeda conjecture.